Chaotic dynamics and superdiffusion in a Hamiltonian system with many degrees of freedom

TL;DR

This paper investigates the Hamiltonian Mean Field model, revealing chaotic behavior, phase transitions, and anomalous diffusion phenomena such as Lévy walks near critical points in a many-degree-of-freedom Hamiltonian system.

Contribution

It provides new insights into the chaotic dynamics and superdiffusive behavior in a fully-coupled particle system with phase transition characteristics.

Findings

Strong chaos at the critical point

Anomalous diffusion and Lévy walks observed

System relaxes to equilibrium after transient superdiffusion

Abstract

We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when the energy is increased. Strong chaos is found in correspondence to the critical point on top of a weak chaotic regime which characterizes the motion at low energies. For a small region around the critical point, we find anomalous (enhanced) diffusion and L\'evy walks in a transient temporal regime before the system relaxes to equilibrium.